Controversy surrounds whether binocular rivalry involves the same mechanisms as those that mediate the bistable perception of ambiguous figures (e.g., Necker cube). During binocular rivalry, discrepant monocular images compete for exclusive perceptual dominance. Using fMRI, Tong and Engel (2001) recently found powerful rivalry-related modulations in monocular visual cortex (V1). This physiological evidence supports the notion that interocular competition mediates binocular rivalry. However, it is still controversial whether some top-down processes may access V1 and mediate stimulus competition. Here we show that attentional modulation of dominance durations during binocular rivalry is limited compared to bistable perception of a Necker cube. In two separate binocular rivalry experiments, we presented rivaling orthogonal gratings or complex meaningful stimuli (i.e. house vs. face). Subjects were instructed to either passively observe the stimuli or try to see one monocular stimulus for as long as possible while reporting their online perception. Stimulus contrast of one monocular image was manipulated. In no case could subjects increase the dominance duration of the desired percept, although they did show a limited ability to shorten the duration of the undesired percept. However, when subjects viewed a Necker cube from one of three fixation-point positions, in all cases subjects could both greatly increase the dominance duration of the desired percept and decrease the dominance duration of the undesired percept. Although previous studies have shown that subjects can control the alternation rate of binocular rivalry (Lack, 1971), our study is the first to test subjects' ability to attentionally bias one visual representation over another. The results suggest that unlike other bistable visual phenomena (e.g., Necker cube), binocular rivalry is resolved in early visual stages and cannot be accessed by high-level attentional processes.